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2015 HiMCM B题特等奖学生论文下载6018

Category: HiMCM数模竞赛, 国际竞赛 Date: 2018年8月11日下午1:12

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论文摘要如下：

18th?Annual?High?School?Mathematical?Contest?in?Modeling?(HiMCM)

Summary?Sheet

(Please?attach?a?copy?of?this?page?to?each?copy?of?your?Solution?Paper.)

Team?Control?Number:?? 6018

Problem?Chose:?? B

Our?model?serves?to?describe?the?safety?of?My?City?with?a?rating?that?can?be?compared? to?the?FBI?Crime?Data?for cities?and?metropolitan?areas. The?FBI data?was?approximated?to? represent?a?normal?distribution,?and?because?the?My?City?data?fit?the?normal?distribution,?the? model?was?able?to?rate My City in?relation?to?the?cities?and?metropolitan?areas?within?the? United?States.?The?model?that?was?used?to?best?represent?that?safety?ranking?was? in which?R? m? ?was?the?rating?of?the?metropolitan?area?and?was?calculated?with( W )R m =Σ c×Cm ? the?summation?of?each?of?the?major?crime’s rate?per 100,000?people?for?two?weeks?multiplied? by?its?individual?weights.?The?weights?were?calculated?by?the?sentence?of?each?crime?using?data? from?the United?States?Sentencing?Commission?by?using?the?median?sentence?given?for?each? crime?used?in?the?safety?ranking.

The?advantage?to?this?rating?system?is?that?it?incorporates?the?frequency?of?crime? occurrences?as?well?as?the?severity?of?the crime?into?the?safety?rating. The?calculated safety? rating?for?My?City?was?1370.9268?and?the?mean?of?the?FBI?metropolitan?area?ratings?was? 1462.467?with?a?standard?deviation of 564.8396.?As?a?result,?the?z-score?of?My?City?in?relation? to?the?population?of?FBI?data?was?-0.1620636,?meaning?that?it?was?safer?than?56.43?percent?of? cities.

In?addition?to?this,?a?city?that?was?most?similar?to?My?City?was?found?based?on?the? safety?rankings?and?population?size?and was?determined?to?be Chicago. Using?GDP?and?crime? data?for?several?years?in?Chicago’s?past,?a?significant?correlation?was?determined?between?the? crime?rate?and?the?GDP of Chicago,?which?was?then?concluded?to?also?apply?to?My?City?due?to? their?similarities.

Also,?using?a?model?to?determine?which?of?the?district?and?beats?had?the?most? dangerous?proportion?of?violent?and property?crime?within?My?City, district-specific values? were?established?that?represented?the?proportion?of?the?My?City?police?force?that?would?be? assigned?to?each?district?in?order?to optimize?the?the?safety?by?placing?more?officers?in?more? dangerous?districts?and?fewer?in?less?dangerous?ones.

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